Question

David deposited $500 at the end of every month into an RRSP for 8 years. The interest rate earned was 4.75% compounded semi-annually for the first 2 years and changed to 5.00% compounded monthly for the next 6 years. What was the accumulated value of the RRSP at the end of 8 years?

Answer #1

Solution :-

Interest rate for first 2 years = 4.75 % ( Compounded Semiannally )

Therefore Monthly interest rate = ( 1 + 0.0475 / 2
)^{1/6} - 1 = 1.00392 - 1 = 0.392%

Now Monthly interest rate after 2 years = 5.00% / 2 = 0.4167%

Now the Future Value of First two years deposit at the end of year 2 =

FV = P * [ (1 + r )^{n} - 1 ] / r

FV = $500 * [ ( 1 + 0.00392 )^{24} - 1 ] / 0.00392

FV = $500 * 25.10697

FV = $12,553.49

FV of the Deposit of first 2 years at the end of year 6 =
$12,553.49 * ( 1 + 0.004167 )^{4*12}

= $12,553.49 * ( 1 + 0.004167 )^{6*12}

= $12,553.49 * 1.349

= $16,865

Now Future Value of Deposit of year 2 - 8 at the end of Year 8

FV = P * [ (1 + r )^{n} - 1 ] / r

FV = $500 * [ ( 1 + 0.004167 )^{72} - 1 ] / 0.004167

FV = $500 * 83.77

FV = $41,885.61

Therefore the Future Value at the end of Year 8 = $16,865 + $41,885.61 = $58,750.62

If there is any doubt please ask in comments

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